Answer:
Specific Gravity = m/[m(s)-m(os)]
Explanation:
Specific gravity, also called relative density, is the ratio of the density of a substance to the density of a reference substance. By this definition we need to find out the ratio of density of the object of mass m to the density of the surrounding liquid.
m = mass of the object
<u>Weight in air</u>
W (air) = mg, where g is the gravitational acceleration
<u>Weight with submerged with only one mass</u>
m(s)g + Fb = mg + m(b)g, <em>consider this to be equation 1</em>
where Fb is the buoyancy force
Weight with submerged with both masses
m(os)g + Fb’ = mg + m(b)g, <em>consider this to be equation 2</em>
<u>equation 1 – equation 2 would give us</u>
m(s)g – m(os)g = Fb’ – Fb
where Fb = D x V x g, where D is the density of the liquid the object is submerged in, g is the force of gravity and V is the submerged volume of the object
m(s)g – m(os)g = D(l) x V x g
m(s) – m(os) = D(l) x V
we know that Mass = Density x V, which in our case would be, D(b) x V, which also means
V = Mass/D(b), where D(b) is the density of the mass
<u>Substituting V into the above equation we get</u>
m(s) – m(os) = [D(l) x m)/ D(b)]
Rearranging to get the ratio of density of object to the density of liquid
D(b)/D(l) = m/[m(s)-m(os)], where D(b)/D(l) denotes the specific gravity
